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Credit risk pricing in a general framework.

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Author

Huang, Hanming.

Date of Issue

2012

School

School of Humanities and Social Sciences

Abstract

In the literature, two principal approaches are widely used for credit risk modeling: structural models and reduced form models.
The evolution of firms’ structural variables, such as firms’ asset and debt values, are applied to determine the time of default in structural models. In these models, a default event occurs when the value of the assets falls below some threshold for the first time.
On the other hand, the reduced-form models avoid the link between the default arrival and firms’ capital structures, and directly apply an exogenous counting process to the default arrival time. Therefore, the default time is usually a totally inaccessible stopping time.
The methodology of this thesis falls into the latter category. In the thesis, a (doubly stochastic) marked Poisson process is introduced to model a sequence of credit event arrivals.And upon each default arrival, a random mark is drawn from the mark space to identify the default event. By the theorem of thinning Poisson process, two independent marked Poisson processes can be separated to model two different kinds of arrivals: a default event with liquidation effect and a default event with non-liquidation effect. This characterization distinguishes our approach from traditional approaches, in which the default event is usually modeled as the first jump of a counting process. Under this setting, a general pricing framework for defaultable claims is provided and it is applied to value defaultable bonds under different recovery schemes.
In the following chapter, we follow a similar methodology to Schönbucher (2000) to derive the drift restrictions in the interest rate analysis framework of Heath, Jarrow and Morton (1992). Different arbitrage free conditions are consequently examined and Girsanov’s theorem is discussed under the marked Poisson framework.
At the end of the thesis, we provide a specification of the model: a Hull-White example. An Ornstein-Uhlenbeck process is applied to model the dynamics of the mean-reversed default free interest rate and the dynamics of the default intensity process. Consequently, analytical solutions for defaultable bonds are derived and other basic credit derivatives, such as credit default swap (CDS) and convertible bonds, are priced under the model specification.